
// Make newform 950.2.bb.e in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_bb();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_bb_e();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_950_bb();"
function MakeCharacter_950_bb()
    N := 950;
    order := 36;
    char_gens := [77, 401];
    v := [27, 34];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_950_bb_Hecke(Kf)
    return MakeCharacter_950_bb();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_bb_e();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_950_2_bb_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_bb();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![110075314176, 47552535724032, 10271347716390912, 1177318888493285376, 71775505495240998912, 945038355634430410752, 6792424919875461316608, 36068343141117942300672, 146309349615376614359040, 418881848745294631010304, 735807979068185301221376, 217512223265093845745664, -2972799885077332035010560, -9619533256188199848984576, -13537890468485177745530880, 5728957729802215620175872, 83463631797267031324119552, 235484836034565869346332160, 341238624784195972460447232, -104687961235109596834868736, -2206796141079222747741628272, -7144893032016970770680866752, -13748870820353003197600156128, -14669968139835436613088104184, 4539775458186041846761280241, 58460688916974764393552276832, 151089804342808685212488735168, 269079306605162070799207383144, 378766006435805086914180911892, 445391367985987480509704903844, 462867988520858191415688542112, 444628292651322343270175404008, 413169883553400018757887523878, 393410359653731107224434250192, 381497351395602703808127710664, 359726423289428905410516842880, 325410149074161124210341576420, 282949114519878231315143656368, 239486797408364575218547349472, 199578546511373976133223226312, 163739928880912389985169984619, 130893021500100995418477938064, 100135449552652875381024612432, 75110225951606864063315657256, 57734795673995568993135821844, 44038969786680889565663728668, 30969946318429905844814546112, 20294151800005354148096578200, 13627244368135153156715520850, 9457475739501663831443144916, 6147470220405602498447057784, 3703050153662796334178905920, 2351626784673805202542300920, 1571248140618190872298614024, 940152721625565281595687024, 478894364922200462275540584, 245213690458092406296201885, 133919769343159606001455908, 61329760818636900496726224, 18798007384274488091351856, 5427204222785755336648212, 2524285506443972187172152, 399178190411880588357264, -777891122439877914564576, -605544958729524465531306, -281768961048873061151748, -157146713003889718638696, -101879598328732982333928, -44352456585939270500796, -12572062470940721517120, -930692366465502628080, 1136217883947120098304, 989810377973209866148, 470139499438678863264, 273996770319629782200, 113910050260760422416, 18830358077437718844, -8920175572664393532, -1343472753785636736, 2629881638139843792, 1802972074344848340, 414184793773991328, -85167711410932656, -96147665471367432, -27409931700419752, 5363936975699280, 1365679940072112, -1339363702298928, -890965487007834, 95863023215700, 131277286256832, 15981342443016, -25391736339000, -13747498978332, -1083145272480, 1131371504184, 819952510588, 78153837828, -1387635768, -11170647600, 1424958300, -579090564, -60856704, -57950232, 15739173, 10388976, -240768, -337368, -1056716, 8988, 7200, -4320, 2682, -192, 0, 120, -36, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;